Calculating Angular Speed of a Shaft with Given Angular Acceleration

In summary, the conversation is about finding the angular speed of a shaft that is initially turning at 73.8 rad/s and has an angular acceleration of -10.1 rad/s2 - 4.44 t rad/s3. The solution involves integrating both sides of the equation dω = αdt and solving for ω using the limits of integration 73.8 to ω and 0 to 2.58.
  • #1
Chuck 86
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0

Homework Statement


A shaft is turning at 73.8 rad/s at time zero. Thereafter, its angular acceleration is given by
a = -10.1 rad/s2 - 4.44 t rad/s3.
where t is the elapsed time. Calculate its angular speed at t = 2.58 s

Homework Equations


1/2(Angular accel formula)+ 73.8t+0= theta final


The Attempt at a Solution


do i take the integral of the accel formula then the velocity the plug in 2.58?
 
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  • #2
You need to integrate both sides of

dω = αdt

The limits of integration should be

73.8 to ω (left side) and 0 to 2.58 (right side)

After you integrate, solve for ω.
 
  • #3
so i set 1/2(angular accel)= 73.8+ theta final? then take the integral?
 
  • #4
so i set 1/2(angular accel)= 73.8+ theta final? then take the integral?
I never said that. I have no idea where you get that 1/2(angular accel) = 73.8 + theta final means something when it is not even dimensionally correct. Do the following integral and solve for ω. That's what I suggested in the first place.

[tex]\int_{73.8}^{\omega}d \omega=\int_{0}^{2.58}(-10.1-4.44 t) dt[/tex]
 
  • #5
whoa dude calm down. i appericiate the help but remember i was just asking a question, i already feel stupid enough as it is
 

1. What is rotational motion of a shaft?

Rotational motion of a shaft refers to the circular movement of a rigid body around its axis. This type of motion is common in machines and engines where the shaft is used to transfer energy or rotate components.

2. How is rotational motion of a shaft measured?

Rotational motion of a shaft is measured using angular displacement, which is the change in the angle of rotation of the shaft. This can be measured using a protractor or other angular measurement tools.

3. What factors affect the rotational motion of a shaft?

The rotational motion of a shaft can be affected by factors such as the torque applied to the shaft, the mass and distribution of the load, and any external forces acting on the shaft.

4. How is rotational motion of a shaft different from linear motion?

Rotational motion of a shaft involves movement around an axis, while linear motion involves movement in a straight line. Additionally, rotational motion is described in terms of angular displacement, velocity, and acceleration, while linear motion is described in terms of displacement, velocity, and acceleration.

5. What are some real-world applications of rotational motion of a shaft?

Rotational motion of a shaft is used in various machines and devices, such as car engines, turbines, and drills. It is also used in everyday objects like wheels, gears, and pulleys to transfer and convert energy.

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